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Fibonacci Retracement

Fibonacci retracement levels are a useful tool that can help you determine how much of a move in a given part of the main trend will retrace before that trend is resumed. Fibonacci retracements have been very useful in gold, silver and mining stocks as well as currency markets.

Eric asks:

Video library; Eric, John and Jill are picking a movie for the evening.

One of the most popular retracement levels is 50% which means that, for instance, in an uptrend, after a move, a temporary reversal takes place, retracing about 50% of it, before the main trend continues. Other popular levels are 33% and 66%.

The Fibonacci sequence is a sequence of numbers discovered by an Italian mathematician Leonardo Fibonacci in the thirteenth century. The sequence is: 1, 1, 2, 3, 5, 8, 13, … etc., or stating it the other way: each term of the sequence is a sum of the previous two.

Be patient Eric, let me explain. It is not about the numbers, it is more about the relationships between them. You see, when you take the ratio of an element of the sequence to its predecessor it approaches 1.618 as we examine further and further elements. This is the so-called golden ratio which is omnipresent in the nature and the society. Take the Da Vinci Code we are about to watch – some of its action takes place in the Louvre and one of its most popular exhibits – Mona Lisa – is a great example of the golden ratio’s presence: her face is a perfect golden rectangle, that is if you take the ratio of her face’s height to its width you get 1.618.

And there is more! If you take the inverse of the golden ratio, that is if you take the ratio of an element to its successor, it approaches 0.618 and this is quite important in terms of Fibonacci retracement levels. But before we proceed, let me mention another important ratio – the ratio of an element to the second closest term, it approaches either 2.618 or 0.382 – depending on whether you divide the larger number by the smaller one or the other way around.

(looking at Eric’s confused expression) Don’t worry, now comes the best part: the application of these ratios. Remember when I mentioned the most popular retracement levels: 33%, 50% and 66%? These Fibonacci ratios are a refinement on these levels: instead of using this set of levels, we use 38,2%, 50% and 61,8% which turn out to be a little more accurate.

The level that should be used is determined by the strength of a trend: in a strong trend 38,2% is most likely, while in a feeble one chances favor 61,8%. A 50% retracement level could be useful in a moderate trend. Previous retracements in the current trend can be a decent indication of the next one’s extent.

Great! I can’t wait to test these levels myself! And now let’s see how the Fibonacci sequence fits into Da Vinci Code’s plot, shall we?

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The idea that after a move in the direction of the main trend, the price retraces some of the covered distance, is quite old. It was already proposed by Charles Dow during his work on the functioning of the stock market, that the breadth of this retracement was from 33% to 66%

This idea was further refined by Ralph Nelson Elliott who employed more accurate retracement levels: 38.2%, 50% and 61.8%, obtained using the Fibonacci sequence – a sequence discovered by an Italian mathematician Leonardo Fibonacci in the thirteenth century.

The Fibonacci Sequence and the Ratios Used as Retracement Levels

The Fibonacci sequence is: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … (it goes on this way to infinity). In other words, each term (starting from the third) is a sum of the two preceding ones: 1+1=2, 1+2=3, 2+3=5, 3+5=8 and so on.

What is more important, in terms of stock market applications, is the way that individual elements of the sequence are related:

The ratio of an element of the sequence to its predecessor approaches 1.618 as we proceed to infinity (the convergence begins to take shape after a couple of elements: 1/1=1, 2/1=2, 3/2=1.5, 5/3=1.667, 8/5=1.6, 13/8=1.625, 21/13=1,615, 34/21=1.619, 55/34=1.618, and so on). This number is called the golden ratio or the phi number and is ubiquitous both in nature (e.g. proportions of human body, the solar system, DNA) and in the society (e.g. art and architecture, music), and – as will be shown later – in the stock market.

The ratio of an element of the sequence to its successor approaches 0.618 as the sequence proceeds to infinity (also in this case the convergence begins to take shape after a couple of terms: 1/1=1, 1/2=0.5, 2/3=0.667, 3/5=0.6, 5/8=0.625, 8/13=0.615, 13/21=0.618, and so on). It is the reciprocal of the phi number.

The ratios of alternate numbers converge to 2.618 or its inverse – 0.382. For instance, 55/21=2.619 and 21/55=0.382.

Two of these ratios are most important when it comes to constructing Fibonacci retracement levels, namely 0.382 and 0.618 (corresponding to 38.2% and 61.8%) which are used instead of the “traditional” 33% and 66% proposed by Dow. This approach suggests that in a very strong trend, prices will retrace approximately 38% after reaching the top or bottom, and before continuing to move further. In a weaker trend, the maximum retracement is around 62% of the previous move.

How the Fibonacci Sequence Was Discovered

Fibonacci came up with this sequence considering a pair of breeding rabbits, or – to be more exact – the number of pairs of rabbits after a particular number of periods.

It is assumed that each pair matures in two months, and produces a new pair every month thereafter, starting at the end of the second month of their life. We also assume that no pair of rabbits dies.

We begin with one pair in Month 1.

In Month 2 there is still a single pair of rabbits. At the end of this month it gives birth to the second pair.

In Month 3 there are two pairs of rabbits, one of them (born last month) is still immature, so only one pair is born at the end of Month 3.

In Month 4 there are three pairs of rabbits, one of which (born last month) is still immature, so only two pairs are born at the end of Month 4.

In Month 5 there are five pairs of rabbits, two of which (born last month) are still immature, so only three pairs are born at the end of Month 5.

If we continue this process, we observe that in a given month, the number of rabbits is equal to the number of rabbits in the previous month (because no pair dies) plus the number of pairs that could be produced two months before (as the rabbits need two months to mature). A table below presents the first 7 months:

Month

0

1

2

3

4

5

6

Number of pairs

1

1

1+1=2

2+1=3

2+3=5

5+3=8

8+5=13

As was stated above the number of pairs can be described by the following formula:

Number of pairs of rabbits in the n-th month = Number of pairs of rabbits in the (n-1)-th month + Number of pairs of rabbits in the (n-2)-th month

Or in a more general way (denoting the n-th term of the sequence by a_n)a_n = a_(n-1) + a_(n-2)

Fibonacci Retracement and Gold

The Fibonacci retracement is a technique that's quite useful on the gold market - the price of the yellow metal often stops its price swings once one of the retracement levels is reached. You can see details on the chart below.

Fibonacci Retracement and Silver

On the chart below we can see an application of the Fibonacci retracement levels to the silver market (charts courtesy of http://stockcharts.com/).

The support levels obtained through the use of Fibonacci retracement levels proved accurate in the analysis of silver price movements. Fibonacci retracement levels for gold have proven very valuable many times as well.

Conclusion

Fibonacci retracement levels prove a useful tool in predicting the breadth of a counter-trend move, after the price reaches a local top and before the main trend is resumed and they serve as important support or resistance levels. They have their foundations in a mathematical relations ubiquitous in nature and in the society, which alone makes them somewhat credible but – what is far more important – can be seen in the stock exchange quite often.

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Related terms:

A pattern, as the word suggests, is something that repeats in a noticeable way. For example, a patterned carpet consists of repeating images that are similar or the same. But there are more useful patterns in our everyday life and, more to the point, patterns that have implications for precious metals investors. Namely, gold price patterns can help us determine the direction in which gold will head next and the same goes for silver.

Phi (Greek letter φ) – also known as the golden number or the golden ratio – is an irrational number, approximately equal to 1.61803399, that can be used to predict market moves, as it is an indispensable element of such tools as Fibonacci retracement levels or Elliott wave theory. It's useful also for gold and silver investors.

Rather than studying fundamental issues, technical traders place their bets according to pure data that is generated from the market. The term “technical” trading applies to a variety of fields from option trading to commodity stocks trading. The purpose of technical analysis is to pinpoint potential pivotal points. It shows when to enter and exit the market.